Convexity for invariant differential operators on semisimple symmetric spaces
Van den Ban, E. P. ; Schlichtkrull, H.
Compositio Mathematica, Tome 89 (1993), p. 301-313 / Harvested from Numdam
Publié le : 1993-01-01
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     author = {van den Ban, E. P. and Schlichtkrull, H.},
     title = {Convexity for invariant differential operators on semisimple symmetric spaces},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {301-313},
     mrnumber = {1255699},
     zbl = {0798.58083},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__89_3_301_0}
}
Van den Ban, E. P.; Schlichtkrull, H. Convexity for invariant differential operators on semisimple symmetric spaces. Compositio Mathematica, Tome 89 (1993) pp. 301-313. http://gdmltest.u-ga.fr/item/CM_1993__89_3_301_0/

[1] E Van Den Ban: A convexity theorem for semisimple symmetric spaces, Pac. J. Math. 124 (1986), 21-55. | MR 850665 | Zbl 0599.22014

[2] E Van Den Ban: Asymptotic behaviour of matrix coefficients related to reductive symmetric spaces, Proc. Kon. Nederl. Akad. Wet 90 (1987), 225-249. | MR 914083 | Zbl 0629.43008

[3] E. Van Den Ban and H. Schlichtkrull: The most continuous part of the Plancherel decomposition for a reductive symmetric space. In preparation.

[4] E. Van Den Ban and H. Schlichtkrull: Multiplicities in the Plancherel decomposition for a semisimple symmetric space. In (R. L. Lipsman e.a. eds) Representation Theory of Groups and Algebras, Contemp. Math., Vol. 145, p. 163-180. Amer. Math. Soc., Providence 1993. | MR 1216188 | Zbl 0809.43004

[5] A. Cérézo and F. Rouvière: Opérateurs différentiels invariants sur un groupe de Lie, Sém. Goulaouic-Schwartz 1972-73 (1973), Exposé X, p. X.1-X.9. | Numdam | MR 430153 | Zbl 0259.58012

[6] W. Chang: Global solvability of the Laplacians on pseudo-Riemannian symmetric spaces, J. Funct. Anal. 34 (1979), 481-492. | MR 556268 | Zbl 0431.58015

[7] W. Chang: Invariant differential operators and P-convexity of solvable Lie groups, Adv. in Math. 46 (1982), 284-304. | MR 683203 | Zbl 0506.22012

[8] J. Dadok: Solvability of invariant differential operators of principal type on certain Lie groups and symmetric spaces, J. d'Anal. Math. 37 (1980), 118-127. | MR 583634 | Zbl 0445.58031

[9] M. Duflo and D. Wigner: Convexité pour les operateurs différentiels invariants sur les groupes de Lie, Math. Zeit. 167 (1979), 61-80. | MR 532886 | Zbl 0387.43007

[10] M. Flensted-Jensen: Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal. 30 (1978), 106-146. | MR 513481 | Zbl 0419.22019

[11] M. Flensted-Jensen: Analysis on Non-Riemannian Symmetric Spaces, Regional Conference Series in Math. 61, Amer. Math. Soc., Providence 1986. | MR 837420 | Zbl 0589.43008

[12] Harish-Chandra: Spherical functions on a semisimple Lie group, I, Amer. J. Math. 80 (1958), 241-310. | MR 94407 | Zbl 0093.12801

[13] S. Helgason: Fundamental solutions of invariant differential operators on symmetric spaces, Amer. J. Math. 86 (1964), 565-601. | MR 165032 | Zbl 0178.17001

[14] S. Helgason: The surjectivity of invariant differential operators on symmetric spaces I, Ann. of Math. 98 (1973), 451-479. | MR 367562 | Zbl 0274.43013

[15] S. Helgason: Groups and Geometric Analysis, Academic Press, Orlando 1984. | MR 754767 | Zbl 0543.58001

[16] S. Helgason: Invariant differential operators and Weyl group invariants. In (W. Barker and P. Sally, eds.) Harmonic Analysis on Reductive Groups, Bowdoin College 1989, Birkhäuser, Boston 1991, p. 193-200. | MR 1168483 | Zbl 0760.43002

[17] L. Hörmander: Linear Partial Differential Operators, Springer Verlag, Berlin 1963. | MR 161012 | Zbl 0108.09301

[18] T. Oshima and J. Sekiguchi: Eigenspaces of invariant differential operators on a semisimple symmetric space, Invent. Math. 57 (1980), 1-81. | MR 564184 | Zbl 0434.58020

[19] J. Rauch and D. Wigner: Global solvability of the Casimir operators, Ann. of Math. 103 (1976), 229-236. | MR 425017 | Zbl 0323.58021

[20] F. Rouvière: Invariant differential equations on certain semisimple Lie groups, Trans. Amer. Math. Soc. 243 (1978), 97-114. | MR 502896 | Zbl 0399.58023

[21] H. Schlichtkrull: Harmonic Analysis on Symmetric Spaces, Birkhäuser, Boston 1984. | MR 757178

[22] F. Treves: Linear Partial Differential Equations, Gordon and Breach, New York 1970. | Zbl 0209.12001

[23] O. Zariski and P. Samuel: Commutative Algebra, Vol. I, Van Nostrand, Princeton 1958. | MR 90581 | Zbl 0081.26501 | Zbl 0121.27801